Nursing Elites

1. Solve the equation 8x − 6 = 3x + 24. Which of the following is the correct solution?

• A. x = 2.5
• B. x = 3.6
• C. x = 5
• D. x = 6

Correct answer: D

Rationale: To solve the equation 8x − 6 = 3x + 24, start by adding 6 to both sides: 8x − 6 + 6 = 3x + 24 + 6, which simplifies to 8x = 3x + 30. Next, subtract 3x from both sides to get 5x = 30. Finally, divide both sides by 5 to solve for x: x = 6. Therefore, the correct solution is x = 6. Choices A, B, and C are incorrect because they do not result from the correct algebraic manipulation of the equation.

2. Solve for x: 2x + 6 = 14

• A. x = 4
• B. x = 8
• C. x = 10
• D. x = 13

Correct answer: A

Rationale: To solve the equation 2x + 6 = 14, you first subtract 6 from both sides to isolate 2x. This gives 2x = 8. Then, divide by 2 on both sides to find x. Therefore, x = 4. Choices B, C, and D are incorrect as they do not correctly follow the steps of solving the equation.

3. What defines a composite number?

• A. A number with only two factors
• B. A number that is a fraction
• C. A number with more than 2 factors
• D. A number with exactly two factors

Correct answer: C

Rationale: A composite number is a positive integer greater than one that has more than two factors. Choice A is incorrect because a number with only two factors is a prime number. Choice B is incorrect as being a fraction does not define a composite number. Choice D is incorrect because a number with exactly two factors is a prime number, not a composite number.

4. What is the equation that describes the relationship between x and y in the table below: x = 2, y = 6; x = 3, y = 9; x = 4, y = 12?

• A. y = 3x
• B. x = 3y
• C. y = x/3
• D. y = x + 3

Correct answer: A

Rationale: The correct answer is y = 3x. By examining the table provided, we can see that for each increase of 1 in x, y increases by 3. This consistent pattern indicates that y is three times the value of x, leading to the equation y = 3x. Choices B, C, and D do not match the pattern observed in the table and are therefore incorrect.

5. If (D) is the distance traveled and (R) is the rate of travel, which of the following represents the relationship between D and R for the equation D=2R?

• A. D is twice as much as R
• B. R is twice as much as D
• C. R is two times D
• D. D is two more than R

Correct answer: A

Rationale: The equation D=2R means that D equals 2 times R, which translates to D being twice the value of R. Therefore, choice A, 'D is twice as much as R,' is the correct representation of the relationship between D and R. Choice B, 'R is twice as much as D,' incorrectly reverses the roles of D and R. Choice C, 'R is two times D,' incorrectly states the relationship between R and D. Choice D, 'D is two more than R,' does not accurately reflect the relationship presented in the equation.

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